Question

One rectangle is twice as long as it is wide. The second rectangle is 3cm longer than the first one, and 1cm narrower than the first one. The areas of both rectangles are the same. What are the dimensions of the first rectangle?

Answer 1

L1 = Length of the first rectangle

W1 = Width of the first rectangle

A1 = Area of the first rectangle

L2 = Length of the second rectangle

W2 = Width of the second rectangle

A1 = Area of the second rectangle


L1 = 2 W1

A1 = L1 * W1 = 2 W1 * W1 = 2 W1 ^ 2

L2 = L1 + 3 = 2 W1 + 3

W2 = W1 - 1

A2 = L2 * W2 = ( 2 W1 + 3 ) * ( W1 - 1 )


A1 = A2

2 W1 ^ 2 = ( 2 W1 + 3 ) * ( W1 - 1 )

2 W1 ^ 2 = 2 W1 * W1 + 3 * W1 - 1 * 2 W1 - 1 * 3

2 W1 ^ 2 = 2 W1 ^ 2 + 3 W1 - 2 W1 - 3

2 W1 ^ 2 = 2 W1 ^ 2 + W1 - 3 Subtract 2 W1 ^ 2 to both sides

2 W1 ^ 2 - 2 W1 ^ 2 = 2 W1 ^ 2 + W1 - 3 - 2 W1 ^ 2

0 = W1 - 3 Add 3 to both sides

0 + 3 = W1 - 3 + 3

3 = W1

W1 = 3 cm

L1 = 2 W1 = 2 * 3 = 6 cm